Fun to watch but...

They do not really make the historical weapons. They make mockerys of them.

I used to do Japanese martial arts so I know a little bit about Katanas. I know that, apart from the shape, there is one specific feature that makes the blade unique and that is the clay method of differential tempering.

As they explained on the show, quenching the hot blade hardens the steel. But it also makes it brittle. The Japanese master blacksmiths found a way around that. They covered the blade in clay. A thin layer of clay on the edge, a thick layer of clay on the back. That way the edge cooled faster than the back because the heat could escape faster through the thin clay. The result of this was a blade that was sharp and hard on the edge but had a back that would not break under any circumstances. In battle cracks might appear on the edge from impact on other swords but the sword would stay sharp and in one piece.

If you look at a real katana you can see this effect on the blade. The edge is different from the back. The edge is almost white and has a slightly "ceramic" look to it while the back looks like normal steel.

Without this it is not a katana. No matter how it looks or what you call it, it is not a katana.

I can't judge the other weapons in the same way because I do not know enough about them but it seems to me that they should really set down strickter rules for what features the finished weapons should have.